System and method for dual tubing well design and analysis cross-reference to related applications

ABSTRACT

Methods and systems for analyzing a well system design including determining a volume change of trapped annular regions based on a plurality of initial temperatures and a plurality of final temperatures and an initial pressure. Analyzing the trapped annular regions to determine an enclosure volume change, a fluid expansion volume, and an annular pressure buildup for a safe well system and generating a graphical representation of the bounds of the safe well system envelop.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority to U.S. Provisional Patent Application 62/891,227, which was filed in the U.S. Patent and Trademark Office on Aug. 23, 2019, which is incorporated herein by reference in their entirely for all purposes.

TECHNICAL FIELD

The present disclosure generally relates to a system and method for providing design considerations for High-Pressure and High-Temperature (HPHT) subterranean oil and gas wells. In particular, the present disclosure relates to systems and methods for the design and analysis of dual tubing wellbore configurations.

BACKGROUND

Wellbores are drilled into the earth for a variety of purposes including tapping into hydrocarbon bearing formations to extract the hydrocarbons for use as fuel, lubricants, chemical production, and other purposes. The oil and gas industry typically drill wellbores through multiple subterranean formations, thereby resulting in the establishment of multiple production zones at various locations along the length of the wellbore. As the tubing extends throughout the wellbore, it can encounter several turns and/or changes in pressure. Such pressure can build up in the tubing and the annulus of the well can cause equipment to rupture.

BRIEF DESCRIPTION OF THE DRAWINGS

In order to describe the manner in which the above-recited and other advantages and features of the disclosure can be obtained, a more particular description of the principles briefly described above will be rendered by reference to specific embodiments thereof which are illustrated in the appended drawings. Understanding that these drawings depict only exemplary embodiments of the disclosure and are not therefore to be considered to be limiting of its scope, the principles herein are described and explained with additional specificity and detail through the use of the accompanying drawings in which:

FIG. 1 is a schematic diagram illustrating an exemplary well system which can employ the methods and systems disclosed herein, in accordance with the present disclosure;

FIG. 2 is a diagram illustrating a subsurface well having multiple tubing strings and casings disposed therein, in accordance with the present disclosure;

FIG. 3A is a flow chart exemplifying the AFE/APB analysis method, in accordance with the present disclosure;

FIG. 3B is a second half of a flow chart exemplifying the AFE/APB analysis method, in accordance with the present disclosure;

FIG. 4 illustrates a design limit envelop for a particular well structure, in accordance with the present disclosure;

FIG. 5A is an illustration depicting a conventional system bus computing system architecture capable of performing methods in accordance with the present disclosure;

FIG. 5B is an illustration depicting a computer system having a chipset architecture capable of performing methods in accordance with; and

FIGS. 6A-C are diagrammatic representations of information associated with an Annulus Pressure Buildup scenario in a steam operation in a dual tubing well configuration.

DETAILED DESCRIPTION

It will be appreciated that for simplicity and clarity of illustration, where appropriate, reference numerals have been repeated among the different figures to indicate corresponding or analogous elements. In addition, numerous specific details are set forth in order to provide a thorough understanding of the examples described herein. However, it will be understood by those of ordinary skill in the art that the examples described herein can be practiced without these specific details. In other instances, methods, procedures, and components have not been described in detail so as not to obscure the related relevant feature being described. Also, the description is not to be considered as limiting the scope of the embodiments described herein. The drawings are not necessarily to scale and the proportions of certain parts may be exaggerated to better illustrate details and features of the present disclosure.

The present disclosure relates to methods and systems for analysis and design considerations in High-Pressure and High-Temperature (HPHT) subterranean oil and gas well systems. In particular, the present disclosure relates to analyses and designs corresponding to dual tubing systems. Specifically, annular fluid expansion within sealed annuli can cause annular pressure buildup within a wellbore. HPHT wellbores can be particularly susceptible to rupture, therefore determining the expected pressure buildup within the annular regions is essential for safe wellbore design.

In order to increase the production of hydrocarbons from a single wellbore, a dual tubing string can be used. Dual tubing string arrangements can allow a single wellbore having tubulars disposed therein to produce from two segregated zones. In at least one instance, dual tubing operations can allow for simultaneous production from more than one producing zone. In the alternative, a dual tubing operation can be used to inject a material into one zone of a wellbore while producing from a second zone of the wellbore, which can assist in preventing backflow from one zone to another. However, the dual tubing configurations can cause trapped annulus fluid expansion (AFE) and trapped annulus pressure buildup (APB) within the enclosed space of the tubing annulus. For example, the systems and methods described herein can be used to determine whether an internal region or an external region for a pair of casing string annuli are open or closed and calculate the APB for the trapped region. Such calculations are required where the temperature of a fluid trapped within an enclosed container, such as the annular space within a well system, changes. As the temperature changes, the pressure within the container can also change due to the expansion or shrinkage of the fluid. The methods and systems described herein can be used to calculate the AFE/APB values caused by temperature change from various operations during a well lifecycle in a dual tubing well system. The calculations made using the methods and systems herein can be applied to well system design and analysis.

FIG. 1 illustrates an exemplary operation well system 100 that can employ the systems and methods disclosed herein. As shown, the operational well system 100 can include a rig 102 located on an earth formation 104. The rig 102 may include a drilling platform 106 and a derrick 108 located on the platform. The derrick 108 may support or otherwise manipulate the position of a first tubing 110 and a second tubing 112 configured to be extended into a wellbore 114 drilled into the earth formation 104. In at least some examples, the wellbore 114 can be a directional well, including one or more bends. While FIG. 1 generally illustrates wellbore 114 as having a single bend, it should be understood that in other applications portions or substantially all of the wellbore 114 may be vertical, deviated, horizontal, and/or curved. Additionally, the wellbore 114 can include a casing 116 which can extend partially or fully to the end of the first tubing 110 and the second tubing 112 of the wellbore 114. In some instances, the systems and methods described herein can be used to design a well system prior to drilling. In the alternative, the systems and methods described herein can be used to analyze well systems 100 which are already disposed within a subterranean formation. Such design and/or analysis can be performed using a computing device 118 located in a control or processing facility 120, as described in greater detail below.

Modifications, additions, or omissions may be made to FIG. 1 without departing from the spirit and scope of the present disclosure. For example, FIG. 1 depicts components of the operational well system 100 in a particular configuration. However, any suitable configuration of components may be used. Furthermore, fewer components or additional components beyond those illustrated may be included in the operational well system 100 without departing from the spirit and scope of the present disclosure. It should also be noted that while FIG. 1 generally depicts a land-based operation, those skilled in the art would readily recognize that the principles described herein are equally applicable to operations that employ floating or sea-based platforms and rigs, without departing from the scope of the disclosure.

FIG. 2 illustrates a detailed view of a subsurface well 200 having two tubing stings and multiple casings disposed therein, analysis of which is compatible with the methods and systems described herein. As illustrated in FIG. 2, deep wells of the instant type can include multiple concentric spaced apart casings 210. The space between consecutive casing pipes creates a plurality of annuli 240. As depicted in FIG. 2, four concentric casings 210 with three annuli 240 therebetween, indicated using single-direction cross-hatching, are disposed within the well 200. In the present example, each annuli 240 is substantially closed at a lower end with cement 250 and sealed off at an upper end to assure that the well fluids contained therein do not escape into the surrounding environment. As such, each of the annuli 240 in the well 200 constitutes an “enclosed annulus” that has been filled with a well fluid, referred to as “trapped annulus fluid.” Arrangements, such as the one illustrated in FIG. 2, typically occur during the completion operations of the well system.

The innermost casing 212 of the well 200 constitutes a production casing, within which the production tubing string(s) are located. As illustrated in FIG. 2, two production tubing strings having different lengths and are disposed within the well 200 and are open at the distal end to different zones, or regions, of the well 200. Tubing structures similar to those depicted in FIG. 2 are referred to as “dual tubing.” In the present example, the longer tubing string 290 is open at a lower region 278, while the shorter tubing string 292 is open at a higher region 280.

Modifications, additions, or omissions may be made to FIG. 2 without departing from the spirit and scope of the present disclosure. It should also be noted that while FIG. 2 generally depicts a vertical well section, those skilled in the art would readily recognize that the principles described herein are equally applicable to operations in inclined well sections, direction well sections, horizontal well sections, and the like without departing from the scope of the present disclosure.

As described above, well fluid that is trapped in the annulus of a well system is considered “trapped annulus fluid.” Trapped annulus fluid expansion and annular pressure buildup (AFE/APB) occur when the temperature of the fluid trapped within an enclosed annulus changes. Unexpected pressure changes due to expansion or shrinkage of a fluid in an enclosed container, such as the trapped annular spaces in a well system, can have catastrophic effects on the well including, but not limited to, well burst or collapse. As such, determining the AFE and APB corresponding to these trapped annular regions is critical to ensuring well integrity during operations conducted throughout a well lifecycle. However, due to the large number of trapped annular regions within a dual-tubing system as shown above, such calculations are exceedingly difficult. The present systems and methods address issues relating to the calculations of trapped AFE and trapped APB in such multi-tubing configurations. Specifically, the systems and methods are designed to calculate the APB of a well system at each of the various trapped annulus regions throughout the length of the well.

In at least one instance, the present method can be used to model different operating conditions having known characteristics of the well analyzed to assure the well's integrity under that operational condition. Such analysis can be performed during the design phase of a new well or can be applied to an existing well to determine its operational integrity. For instance, where a production scenario is analyzed, such as that illustrated in FIG. 2, in which each of the dual tubing strings is used to produce hydrocarbon from deep within the formation (such as regions 278 and 280 as shown in FIG. 2) the present methods can be used to determine whether the well system will be prone to burst or collapse.

An exemplary analysis is provided in FIGS. 3A-3B, including iterative calculations to determine the AFE/APB throughout each trapped region within the well system using a computing system described in greater detail below. The analysis includes two iterative loops. In the inner iteration loop, the AFE/APB is calculated for each trapped region throughout the wellbore until the change of storage volume of each region equals the volume change of the fluid by expansion/shrinkage for that region. The outer iteration loop calculates the global AFE/APB for the well system as whole until all trapped regions of the well system reaches a balanced pressure status. In these regards, the pressure changes take into account the following aspects. The change in the volume of a particular region (the trapped/enclosed space volume) due to the change in pressure and temperature compared to the initial conditions. This is due to the effect of Hooke's Law (compressed string steel from increased pressure), the thermal expansion/shrinkage of the steel, and also the ballooning effect. Such AFE/APB calculations can be performed using two well system states referred to herein as initial and final conditions. In at least one instance, the initial and final conditions can correspond to an original and an ending state of an operation.

Specifically, FIGS. 3A and 3B illustrate an exemplary method 300 for calculating pressures in a well system having one or more trapped annulus regions. The method 300 can begin at block 302, as shown in FIG. 3A, where the initial temperature(s) and pressure(s) and the final temperature(s) for each enclosed annulus throughout the wellbore is determined or assumed. In at least one instance, “initial” temperature and pressure can refer to the undisturbed subterranean condition (such as an undisturbed geothermal temperature and static pressure) or drilling operation temperature or pressure, or a production operation temperature and/or pressure. In at least one instance, “final” temperature and pressure can refer to a wellbore condition during a drilling, production, or other wellbore operation.

In at least one instance, the initial temperature(s) and pressure(s) can be measured using one or more sensors. In the alternative, the initial temperature(s) and pressure(s) can be assumed as approximately equal to the temperature and pressure of the earth formation in which the well is located. Additionally at block 302 the final temperature(s) is determined. For example, temperatures within wellbores can change in a gradient. For instance, the formation can get warmer as the wellbore descends. As such, the temperatures throughout the wellbore can be “known,” based on the expected temperature gradient throughout the length of the wellbore. In addition, the fluid type, pressure, and density corresponding to the initial temperature within the enclosed annulus can also be determined or assumed. The method 300 can be used to evaluate the integrity of a dual tubing system such as that illustrated with respect to FIG. 2. In at least one instance, the dual tubing system can be used to produce from two locations within a wellbore. In such instance, a changed temperature gradient can be applied to the well as the fluid moves up within the tubing to estimate the initial and final temperatures. In other instances, the analytical method 300 can be utilized in more complicated scenarios. Such as a stimulation in which hot steam is injected down through a first tubing (such as tubing 290 of FIG. 2) and into the formation to “stimulate” hydrocarbon production up through a second tubing (such as tubing 292 of FIG. 2). In this case, the calculation of the vertical temperature gradient is significantly more complicated, but nonetheless calculable using known methods to arrive at the necessary initial and final temperatures, pressures, and densities.

At block 304, the final pressure(s) are estimated as well as the fluid type and density for each annulus.

While the initial and final temperatures and pressures are defined as specific well conditions above, it should be understood that both the initial and final condition can be any state of the well life cycle.

The tubing strings and casings used in the well system must be strong enough to prevent burst or collapse when the well system is operating. As described above, a trapped annular region occurs where a well fluid is enclosed within an annulus between two casings. To assure a sufficiently robust well design, the effects of pressure buildup in each of the trapped annular regions of the enclosed annuli throughout the length of the wellbore must be computed under the conditions identified in steps 302 and 304. In order for the method 300 to balance the well system as a whole, at block 306, each of the trapped annular regions within the system are identified. Referring back to FIG. 2, such regions can include trapped annular regions filled with well fluid and closed off with packers. Because the temperature gradient and density of the trapped fluid within the enclosed annulus is known (as determined above), the expanded volume and pressure of the trapped annular region and trapped annulus fluid can be calculated. At block 308, a single trapped annular region is selected for analysis.

Since the size and spacing of the casings are known, the interior volume of the “enclosure” can easily be calculated. For example, the length of each casing and location of cement, packer, or other sealing device are considered known as a user performing the simulation can provide such variables to the program. Additionally, the elasticity of the enclosure must be considered as well as any relevant exterior forces acting thereupon. At block 310, the method 300 determines whether the type of trapped region, or enclosure, being analyzed. Specifically, if the trapped annulus is a casing annulus, where the material on either side of the enclosure is a casing, the method 300 can proceed to block 312 where the volume change of the casing annulus is determined based on the original volume of the trapped space. In the alternative, if the trapped space is a tubing annulus, where the annulus is disposed between two tubing strings or between a tubing string and a casing, the method 300 can proceed to block 314 where the volume change must be determined for both the tubing and the surrounding casings. It should be appreciated that it is not only “burst” strength of the enclosure that is relevant, but collapse of the trapped space can also occur and therefore must be taken into account. For example, in analyzing a trapped region such as an enclosed annulus about the production strings, such as that illustrated as region 270 in FIG. 2, the pressure can “press” into the tubing volume, effectively increasing the volume of the trapped space, and as a result, buffer the pressure buildup.

The change in volume of the enclosed space for either block 312 or block 324 can be represented by the following function based on temperature and pressure:

dV _(s) =f(P,T,dP,dT, . . . )

It should be understood that the calculations of volume change in both block 312 and block 314 are determined without reference to the fluid enclosed therein.

The method 300 can then proceed to block 316, where the annular fluid expansion (AFE) due to temperature change is determined for the fluid enclosed within the trapped region selected for analysis. Specifically, using the known values for temperature and pressure, as well as the density/compressibility of the entrapped well fluid, the expansion or shrinkage of the fluid in response to temperature changes can be determined. For example, the change in the volume of the entrapped fluid caused by the temperature change can be expressed by the following function:

dV _(f) =f(dT,V, . . . )

Once the change in volume of the entrapped fluid is determined, the method 300 can proceed to block 318, as illustrated in FIG. 3B, where the pressure change within the trapped region can be calculated. Specifically, at block 318, the annular pressure change (or APB), which is typically an increase, within the enclosure is calculated. In addition, the capability of the enclosure to satisfactorily contain the pressure can be determined. For example, the APB for a balanced enclosure is determined, where dV_(s)=dV_(f) as explained in detail below.

The conditions that determine the APB, or pressure increase, are those in existence when the volume change of the enclosure equals the volume change of the entrapped fluid (expansion/shrinkage), as calculated in steps 312-316 above. This can be expressed by the following function:

APB=dP=f(dV _(f) dV _(s) ,dT, . . . )

For example, when the temperature increases, the trapped fluid expands. If the enclosed volume did not change, then fluid volume (AFE) will not be changed, and the pressure will be increased in order to compress the “expanded” fluid volume to return to the original fluid volume. In such case, since the pressure is increased, the enclosed space volume is be enlarged. The changes need to be balanced so that the changed enclosed space volume is equal to the change of the fluid volume from the temperature. For example, the volume of the enclosure dV_(s) is compared to the calculated volume of the entrapped fluid dV_(f). If dV_(s)=dV_(f), the trapped region is balanced. However, if dV_(s)*dV_(f), the pressure must be changed in order to achieve a balanced trapped region. Specifically, if the enclosure of the trapped area does not have an enclosure volume change (dV_(s)=0), this indicates that the enclosure is rigid. However, the fluid trapped within the enclosure can be subject to expansion and shrinkage as a result of temperature change (dV_(f)≠0). In order for the fluid to remain within the enclosure, a pressure is applied to compress the fluid into the available enclosure volume. The pressure that is applied to the fluid is the APB. However, where the enclosure volume can change due to deformation of the tubing string or casing (i.e., in response to the pressure applied to the tubing string or casing and the ballooning/anti-ballooning effect) and APB work against one another. When the APB is too low, the enclosure volume change can be too small to contain the expanded fluid. As such, increasing the pressure within the enclosure can reduce the fluid expansion volume so that the enclosure is balanced. Once the trapped region is balanced, the method 300 can proceed to block 320.

At block 320, the method 300 determines whether there are additional trapped regions within the well system For example, if there are additional trapped regions the volume change of the enclosure, AFE, and APB must be calculated for each. In such case, the method 300 returns to block 308 where a next trapped region is selected and the process is repeated. The calculation is reiterated until a volume change, AFE, and APB has been calculated for each trapped region existing within the well system, completing the inner loop of the method 300. Once the calculations are complete, the method 300 can proceed to block 322, where the calculations are updated and recorded for each region.

At block 324, the method 300 can then determine whether the well system is balanced for all of the trapped annular regions. It should be appreciated that adjacent enclosed annuli can affect one another; such affects are taken into account in this outer loop of the present method. Specifically, the pressure buildup in each of the annular regions throughout the well bore must be balanced to prevent well rupture. For example, the inner annulus and outer annulus of a casing can both be subject to pressure changes, the ballooning effect of one annulus will affect the APB for both sides of the casing. The balancing step is necessary to ensure the ballooning effect is applied to both sides of the casing globally. For example, when the APB for a first region is calculated as described above, it is assumed that the pressure applied on the other side of the surrounding string is constant. However, when taking each of the trapped annular regions into account the effect of a first trapped annular region on a second trapped annular region that shares a casing or tubing string wall must be taken into account. Due to the shared wall, an enclosure volume change in the first region has a clear effect on the enclosure volume of the second region, which can result in one or both regions becoming unbalanced. Therefore, the AFE and APB calculations must be iterated taking the adjacent trapped annular regions into account.

Referring to the example illustrated in FIG. 2, trapped annular regions exist. The calculation of volume change, AFE, and APB for the annulus about the dual tubing strings (illustrated as region 270) can be complicated due to the presence of multiple tubing strings as well as several additional trapped annular regions (illustrated as regions 272, 274, 276) enclosed by packers. Each entrapped annular region can have a substantial impact on the overall well design or integrity analysis of an existing well. If the well system is not balanced throughout each of the trapped regions, the method 300 returns to block 308, and the calculations are repeated until a balance is achieved.

Once the well system is balanced, the method 300 can proceed to block 326, where the data obtained from the above calculations is output for each of the trapped annular regions. An exemplary output showing typical results is provided as Table 1, below.

TABLE 1 Pressure Volume Differential Differential Region Due to AFE Due to AFE String Annulus Top (ft) Base (ft) (psi)* (bbl)** 20″ Surface Casing Region 1 40.0 450.0 2346.00 1.2 16″ Intermediate Casing Region 1 40.0 6000.0 4365.00 15.4 13⅜″ Protective Casing Region 1 40.0 9200.0 5198.00 9.7 10¾″ Production Tieback Region 1 40.0 14000.0 6324.00 6.5 4½″ Production Tubing Region 1 40.0 12000.0 9369.00 15.4 3½″ Production Tubing *Pressure change caused solely by the Annular Fluid Expansion (AFE) phenomenon **Volume change caused solely by the Annular Fluid Expansion (AFE) effect

As indicated in Table 1, the pressure change due to annular fluid expansion within an entrapped region can be extremely high, such as on the order of thousands of pounds per square inch (psi). As described above, such pressure changes can have a dramatic impact on the safety of the resulting well system. Calculation of the AFE/APB effect is therefore crucial during well system design and analysis in order to produce a well system that is safe throughout the well lifecycle and operations including, but not limited to, circulation, injection, and production. In at least one example, the method 300 can be implement using advanced tubular design software for design and analysis of tubular wellbores. In addition to well system design, the present methods can be implemented on an existing well to determine the integrity of the well system and ability of the well to perform one or more operations.

In at least one instance, the data generated above can be used to produce a graphical representation of the bounds of a safe wellbore. Specifically, the information can be applied to the design of a well system, such as those described above including multiple tubing strings, using the worst-case scenario design principle. Accompanying FIG. 4 provides a graphical representation of the corresponding design limit. For example, the graph depicts an envelop encompassing the bounds of a safe well system design for the well depicted in FIG. 2. Specifically, the simulation illustrated in FIG. 4 provides design limits for a 10¾ inch production tieback having an outer diameter of 10.750 inches. The graph illustrates the well wherein a steam injection operation is performed using the longer tubing 290 and a production operation is performed using the shorter tubing 292.

In the graph, the initial conditions are represented using a solid line having circular data points. Using worst-case design principles, the effect of APB is demonstrated on the graph. It has been shown that once the APB is applied to a simulation, the initial safe design can become unsafe as indicated by the load points outside the safety design limit envelop 400. When this occurs, the string must be redesigned in order to assure safe well integrity. In FIG. 4, the “Max Collapse,” illustrated by a dashed line and square data points, indicates where the APB pressure is applied to the external pressure of the string; “Max Burst,” indicated with a dash-dot line and diamond data points, indicates where the APB pressure is applied to the internal pressure of the string; and “AFE,” illustrated by a dashed line and triangular data points, indicates where both internal and external pressures are applied in the establishment of APB. Specifically, in the present graphical representation, the items 400, 410, 420, 430 are safety design limit envelops based on various criteria, a safe design is located in the overlap of each of these envelops. For example, 400 represents API collapse limit, 410 represents the von Mises envelope, 420 represents API burst limit, 430 represents tension limit, and 440 represents the load condition of the string in the envelop. A well system design is safe and functional for the temperatures and pressures within the envelop. However, the design will fail if the well system experiences temperature and pressure changes which results in a load condition of the string outside the envelop. As such, the method 300 described above can generate a graphical representation of the temperatures and pressure a well system can experience without failure. Such graphs can be used to confirm the safety of a design or to encourage adjustments to the design (including, but not limited to, material selection; wellbore, tubing, and casing reselection; packer placement; annular fluid selection; and any other design change that can have an impact on enclosure volume, fluid expansion, and pressure, and the strength of the strings.). In order to ensure the design is safe for the lifecycle of the well system, several pair of initial conditions and final conditions which can be encountered during the well system lifecycle can be applied to calculate the APB/AFE to ensure the design is safe.

In the alternative, if the method 300 is used to evaluate the integrity of a pre-existing well system, the graphical representation produced can be used to determine safe operating conditions. In addition, the graphical representation can provide an indication of which operating conditions will cause the well system to fail.

Simulations as described above can be completed on a computing device using an advanced tubular design software suite for well system design and analysis. Typical well design software only provides a stress analysis for a single tubing string well system, but cannot provide the detailed analysis of a multi-string well system as described above. In at least one instance, the advanced software can be integrated into current software, such as WELLCAT, DWP, or other related software programs to enhance the program's capacity for design and analysis. Simulations, such as those described above, can be performed using a computing device 118 such as that described with respect to FIG. 1. Exemplary computing devices capable of performing the methods described herein are described in detail below.

Processing facility 120 and computing device 118 may include any suitable computer, controller, or data processing apparatus capable of being programmed to carry out the method, system, and apparatus as further described herein. FIGS. 5A and 5B illustrate exemplary processing facility 120 and computing device 118 that can be employed to practice the concepts, methods, and techniques disclosed herein. The more appropriate embodiment will be apparent to those of ordinary skill in the art when practicing the present technology. Persons of ordinary skill in the art will also readily appreciate that other system embodiments are possible.

FIG. 5A illustrates a conventional system bus computing system architecture 500 wherein the components of the system are in electrical communication with each other using a bus 505. System 500 can include a processing unit (CPU or processor) 510 and a system bus 505 that couples various system components including the system memory 515, such as read only memory (ROM) 520 and random access memory (RAM) 535, to the processor 510. The system 500 can include a cache of high-speed memory connected directly with, in close proximity to, or integrated as part of the processor 510. The system 500 can copy data from the memory 515 and/or the storage device 530 to the cache 512 for quick access by the processor 510. In this way, the cache 512 can provide a performance boost that avoids processor 510 delays while waiting for data. These and other modules can control or be configured to control the processor 510 to perform various actions. Other system memory 515 may be available for use as well. The memory 515 can include multiple different types of memory with different performance characteristics. In at least one instance, the memory 515 can include a well design system, such as WELLCAT, as well as a APB simulation module to assist in the analysis described herein. It can be appreciated that the disclosure may operate on a computing device 500 with more than one processor 510 or on a group or cluster of computing devices networked together to provide greater processing capability. The processor 510 can include any general purpose processor and a hardware module or software module, such as first module 532, second module 534, and third module 536 stored in storage device 530, configured to control the processor 510 as well as a special-purpose processor where software instructions are incorporated into the actual processor design. The processor 510 may essentially be a completely self-contained computing system, containing multiple cores or processors, a bus, memory controller, cache, etc. A multi-core processor may be symmetric or asymmetric.

The system bus 505 may be any of several types of bus structures including a memory bus or a memory controller, a peripheral bus, and a local bus using any of a variety of bus architectures. A basic input/output (BIOS) stored in ROM 520 or the like, may provide the basic routine that helps to transfer information between elements within the computing device 500, such as during start-up. The computing device 500 further includes storage devices 530 or computer-readable storage media such as a hard disk drive, a magnetic disk drive, an optical disk drive, tape drive, solid-state drive, RAM drive, removable storage devices, a redundant array of inexpensive disks (RAID), hybrid storage device, or the like. The storage device 530 can include software modules 532, 534, 536 for controlling the processor 510. The system 500 can include other hardware or software modules. The storage device 530 is connected to the system bus 505 by a drive interface. The drives and the associated computer-readable storage devices provide non-volatile storage of computer-readable instructions, data structures, program modules and other data for the computing device 500. In one aspect, a hardware module that performs a particular function includes the software components shorted in a tangible computer-readable storage device in connection with the necessary hardware components, such as the processor 510, bus 505, and so forth, to carry out a particular function. In the alternative, the system can use a processor and computer-readable storage device to store instructions which, when executed by the processor, cause the processor to perform operations, a method or other specific actions. The basic components and appropriate variations can be modified depending on the type of device, such as whether the device 500 is a small, handheld computing device, a desktop computer, or a computer server. When the processor 510 executes instructions to perform “operations,” the processor 510 can perform the operations directly and/or facilitate, direct, or cooperate with another device or component to perform the operations.

To enable user interaction with the computing device 500, an input device 545 can represent any number of input mechanisms, such as a microphone for speech, a touch-sensitive screen for gesture or graphical input, keyboard, mouse, motion input, speech and so forth. An output device 542 can also be one or more of a number of output mechanisms known to those of skill in the art. In some instances, multimodal systems can enable a user to provide multiple types of input to communicate with the computing device 500. The communications interface 540 can generally govern and manage the user input and system output. There is no restriction on operating on any particular hardware arrangement and therefore the basic features here may easily be substituted for improved hardware or firmware arrangements as they are developed.

Storage device 530 is a non-volatile memory and can be a hard disk or other types of computer readable media which can store data that are accessible by a computer, such as magnetic cassettes, flash memory cards, solid state memory devices, digital versatile disks (DVDs), cartridges, RAMs 525, ROM 520, a cable containing a bit stream, and hybrids thereof.

The logical operations for carrying out the disclosure herein may include: (1) a sequence of computer implemented steps, operations, or procedures running on a programmable circuit with a general use computer, (2) a sequence of computer implemented steps, operations, or procedures running on a specific-use programmable circuit; and/or (3) interconnected machine modules or program engines within the programmable circuits. The system 500 shown in FIG. 5A can practice all or part of the recited methods, can be a part of the recited systems, and/or can operate according to instructions in the recited tangible computer-readable storage devices.

One or more parts of the example computing device 500, up to and including the entire computing device 500, can be virtualized. For example, a virtual processor can be a software object that executes according to a particular instruction set, even when a physical processor of the same type as the virtual processor is unavailable. A virtualization layer or a virtual “host” can enable virtualized components of one or more different computing devices or device types by translating virtualized operations to actual operations. Ultimately however, virtualized hardware of every type is implemented or executed by some underlying physical hardware. Thus, a virtualization compute layer can operate on top of a physical compute layer. The virtualization compute layer can include one or more of a virtual machine, an overlay network, a hypervisor, virtual switching, and any other virtualization application.

The processor 510 can include all types of processors disclosed herein, including a virtual processor. However, when referring to a virtual processor, the processor 510 includes the software components associated with executing the virtual processor in a virtualization layer and underlying hardware necessary to execute the virtualization layer. The system 500 can include a physical or virtual processor 510 that receives instructions stored in a computer-readable storage device, which causes the processor 510 to perform certain operations. When referring to a virtual processor 510, the system also includes the underlying physical hardware executing the virtual processor 510.

FIG. 5B illustrates an example computer system 550 having a chipset architecture that can be used in executing the described method and generating and displaying a graphical user interface (GUI). Computer system 550 can be computer hardware, software, and firmware that can be used to implement the disclosed technology. System 550 can include a processor 555, representative of any number of physically and/or logically distinct resources capable of executing software, firmware, and hardware configured to perform identified computations. Processor 555 can communicate with a chipset 560 that can control input to and output from processor 555. Chipset 560 can output information to output device 565, such as a display, and can read and write information to storage device 570, which can include magnetic media, and solid state media. Chipset 560 can also read data from and write data to RAM 575. A bridge 580 for interfacing with a variety of user interface components 585 can include a keyboard, a microphone, touch detection and processing circuitry, a pointing device, such as a mouse, and so on. In general, inputs to system 550 can come from any of a variety of sources, machine generated and/or human generated.

Chipset 560 can also interface with one or more communication interfaces 590 that can have different physical interfaces. Such communication interfaces can include interfaces for wired and wireless local area networks, for broadband wireless networks, as well as personal area networks. Some applications of the methods for generating, displaying, and using the GUI disclosed herein can include receiving ordered datasets over the physical interface or be generated by the machine itself by processor 555 analyzing data stored in storage 570 or RAM 575. Further, the machine can receive inputs from a user via user interface components 585 and execute appropriate functions, such as browsing functions by interpreting these inputs using processor 555.

It can be appreciated that systems 500 and 550 can have more than one processor 510, 555 or be part of a group or cluster of computing devices networked together to provide processing capability. For example, the processor 510, 555 can include multiple processors, such as a system having multiple, physically separate processors in different sockets, or a system having multiple processor cores on a single physical chip. Similarly, the processor 510 can include multiple distributed processors located in multiple separate computing devices, but working together such as via a communications network. Multiple processors or processor cores can share resources such as memory 515 or the cache 512, or can operate using independent resources. The processor 510 can include one or more of a state machine, an application specific integrated circuit (ASIC), or a programmable gate array (PGA) including a field PGA.

Methods according to the aforementioned description can be implemented using computer-executable instructions that are stored or otherwise available from computer readable media. Such instructions can comprise instructions and data which cause or otherwise configured a general purpose computer, special purpose computer, or special purpose processing device to perform a certain function or group of functions. Portions of computer resources used can be accessible over a network. The computer executable instructions may be binaries, intermediate format instructions such as assembly language, firmware, or source code. Computer-readable media that may be used to store instructions, information used, and/or information created during methods according to the aforementioned description include magnetic or optical disks, flash memory, USB devices provided with non-volatile memory, networked storage devices, and so on.

For clarity of explanation, in some instances the present technology may be presented as including individual functional blocks including functional blocks comprising devices, device components, steps or routines in a method embodied in software, or combinations of hardware and software. The functions these blocks represent may be provided through the use of either shared or dedicated hardware, including, but not limited to, hardware capable of executing software and hardware, such as a processor 510, that is purpose-built to operate as an equivalent to software executing on a general purpose processor. For example, the functions of one or more processors represented in FIG. 5A may be provided by a single shared processor or multiple processors (use of the term “processor” should not be construed to refer exclusively to hardware capable of executing software). Illustrative embodiments may include microprocessor and/or digital signal processor (DSP) hardware, ROM 520 for storing software performing the operations described below, and RAM 535 for storing results. Very large scale integration (VLSI) hardware embodiments, as well as custom VLSI circuitry in combination with a general-purpose DSP circuit, may also be provided.

The computer-readable storage devices, mediums, and memories can include a cable or wireless signal containing a bit stream and the like. However, when mentioned, non-transitory computer-readable storage media expressly exclude media such as energy, carrier signals, electromagnetic waves, and signals per se.

Devices implementing methods according to these disclosures can comprise hardware, firmware and/or software, and can take any of a variety of form factors. Such form factors can include laptops, smart phones, small form factor personal computers, personal digital assistants, rackmount devices, standalone devices, and so on. Functionality described herein also can be embodied in peripherals or add-in cards. Such functionality can also be implemented on a circuit board among different chips or different processes executing in a single device.

The instructions, media for conveying such instructions, computing resources for executing them, and other structures for supporting such computing resources are means for providing the functions described in the present disclosure. In at least one instance, the computing system for implementing the present disclosure can include a memory as described above, one or more programs including an APB simulation program and a well design program, and an interface (including, but not limited to an output device or GUI as described above). In at least one instance, the APB simulation module can include a plurality of sub-modules which are capable of evaluating various aspects of the well system which can be effected by APB. For example, the plurality of sub-modules can include, but are not limited to, a drilling prediction module, a production prediction module, a casing stress module, a tubing stress module, and a multi-string module. The memory can store the application programs, which may also be described as program modules containing computer-executable instructions, executed by the computing device for implementing the present disclosure.

Specifically, a user can input starting parameters including, but not limited to, initial temperatures and pressures corresponding to the well system to be simulated. The computing device can use the well design system to create a diagrammatic representation of the desired well system and the APB simulation module to simulate the pressure changes the well system will experience. The computing device can then proceed with the method 300 as described above to determine a balanced system using the initial well system inputs provided by the user. In at least one instance, the computing device as described above can provide a graphical representation of the simulation, as illustrated in FIGS. 6A-6C. Specifically, FIG. 6A illustrates a graphical representation of the section reference plan through the wellhead origin on azimuth 0.0. The computing display can also provide a diagrammatic representation of a horizontal well system. FIG. 6B illustrates a dual-tubing completion operation. As indicated, the well system being simulated in the present example is a two-string system having packers disposed within the annuli. FIG. 6C illustrates a graphical representation of axial load effect of the tubing strings of FIG. 6B. The simulation provides information corresponding to the annulus fluid expansion. In at least one example, additional information can be displayed to a user regarding the fluid expansion as well as pressure buildup in various trapped regions throughout the length of the wellbore.

Numerous examples are provided herein to enhance understanding of the present disclosure. A specific set of statements are provided as follows.

Statement 1: A method for designing a well system envelop, the method comprising creating an initial design for a well system including two or more tubing strings disposed within a well, the well system including one or more trapped annular regions therein, each of the one or more trapped annular regions including an enclosure; determining a plurality of initial temperatures, a plurality of final temperatures, and an initial pressure for each of the one or more trapped annular regions; estimating a final pressure for each of the one or more trapped annular regions; analyzing each of the one or more trapped annular regions; and generating a wellbore system envelop based at least in part on the analysis of each of the one or more trapped annular regions.

Statement 2: A method in accordance with Statement 1, wherein analyzing the one or more trapped annular regions further comprises selecting a first trapped region from the one or more trapped annular regions; calculating an enclosure volume change for the first trapped region; and calculating an annular fluid expansion (AFE) of a well fluid contained within the enclosure of the first trapped region, the AFE corresponding to a fluid volume change caused by a temperature change.

Statement 3: A method in accordance with Statement 1 or Statement 2, wherein analyzing the one or more trapped annular regions further comprises determining an annular pressure buildup (APB) corresponding to the first trapped region, wherein when the enclosure volume change for the first trapped region is balanced with the AFE for the first trapped region.

Statement 4: A method in accordance with Statements 1-3, further comprising calculating a plurality of APBs corresponding to each of the plurality of initial temperatures and the plurality of final temperatures.

Statement 5: A method in accordance with Statements 1-4, wherein when the well system further includes at least two casings the enclosure of the one or more trapped annular regions includes one or more casing enclosures between two casings, one or more casing and tubing enclosures between a casing and a tubing string, and one or more tubing enclosures between two tubing strings.

Statement 6: A method in accordance with Statements 1-5, further comprising calculating a respective enclosure volume change, a plurality of respective AFEs, and a plurality of respective APBs for each of the remaining one or more trapped annular regions.

Statement 7: A method in accordance with Statements 1-6, further comprising iterating the calculations of the plurality of respective APBs for each of the one or more trapped annular regions assuming a non-rigid enclosure.

Statement 8: A method in accordance with Statements 1-7, further comprising determining whether a global pressure of the well system is balanced for each of the one or more trapped annular regions within the well system based on the non-rigid enclosures.

Statement 9: A method in accordance with Statements 1-8, further comprising generating a graphical representation of the of the wellbore system envelop showing a safe design limit, and transmitting the graphical representation to an output device.

Statement 10: A method in accordance with Statements 1-9, wherein the plurality of initial temperatures, the initial pressure, and the plurality of final temperatures for each of the one or more trapped annular regions are determined using calculations and/or simulation.

Statement 11: A non-transitory computer-readable storage medium storing computer-executable instructions which, when executed by one or more processors, cause the one or more processors to create initial design for a well system including two or more tubing strings disposed within a well, the well system including one or more trapped annular regions therein, each of the one or more trapped annular regions including an enclosure; determine a plurality of initial temperatures, a plurality of final temperatures, and an initial pressure for each of the one or more trapped annular regions; estimate a final pressure for each of the one or more trapped annular regions; analyze each of the one or more trapped annular regions; and generate a wellbore system envelop based at least in part on the analysis of each of the one or more trapped annular regions.

Statement 12: A non-transitory computer-readable storage medium in accordance with Statement 11, wherein the instructions further cause the processor to select a first trapped region from the one or more trapped annular regions; calculate an enclosure volume change for the first trapped region; and calculate an annular fluid expansion (AFE) of a well fluid contained within the enclosure of the first trapped region, the AFE corresponding to a fluid volume change caused by a temperature change.

Statement 13: A non-transitory computer-readable storage medium in accordance with Statement 11 or Statement 12, wherein the instructions further cause the processor to determine an annular pressure buildup (APB) corresponding to the first trapped region, wherein the enclosure volume change for the first trapped region is balanced with the AFE for the first trapped region.

Statement 14: A non-transitory computer-readable storage medium in accordance with Statements 11-13, wherein the instructions further cause the processor to calculate a plurality of APBs corresponding to each of the plurality of initial temperatures and the plurality of final temperatures.

Statement 15: A non-transitory computer-readable storage medium in accordance with Statements 11-14, wherein when the well system further includes at least two casings the enclosure of the one or more trapped annular regions includes one or more casing enclosures between two casings, one or more casing and tubing enclosures between a casing and a tubing string, and one or more tubing enclosures between two tubing strings.

Statement 16: A non-transitory computer-readable storage medium in accordance with Statements 11-15, wherein the instructions further cause the processor to calculate a respective enclosure volume change, a plurality of respective AFEs, and a plurality of respective APBs for each of the remaining one or more trapped annular regions.

Statement 17: A non-transitory computer-readable storage medium in accordance with Statements 11-16, wherein the instructions further cause the processor to iteratively calculate a plurality of respective APBs for each of the one or more trapped annular regions assuming a non-rigid enclosure.

Statement 18: A non-transitory computer-readable storage medium in accordance with Statements 11-17, wherein the instructions further cause the processor to determine whether a global pressure of the well system is balanced for each of the one or more trapped annular regions within the well system based on the non-rigid enclosures.

Statement 19: A non-transitory computer-readable storage medium in accordance with Statements 11-18, wherein when the well system is balanced the instructions further cause the processor to generate a graphical representation of the well system envelop showing a safe design limit; and display the well system envelop and the safe design limit on an output device communicatively coupled with the one or more processors.

Statement 20: A non-transitory computer-readable storage medium in accordance with Statements 11-19, wherein the plurality of initial temperatures, the initial pressure, and the plurality of final temperatures for each of the one or more trapped annular regions are determined using calculations and/or simulation.

Statement 21: A system comprising a well system including a wellbore having at least two tubing strings and at least one casing disposed therein, the well system including a plurality of trapped annular regions, each of the plurality of trapped annular regions being a non-rigid enclosure; one or more processors coupled with an input device; and at least one non-transitory computer-readable storage medium storing instructions which, when executed by the one or more processors, cause the one or more processors to receive a plurality of initial temperatures, an initial pressure, and a plurality of final temperatures corresponding to each of the plurality of trapped annular regions from one or more sensors located within the wellbore of the well system; estimate a final pressure for each of the one or more trapped annular regions; analyze each of the one or more trapped annular regions; and generate an integrity report for the well system, wherein the integrity report is based at least in part on the analysis of each of the plurality of trapped annular regions.

Statement 22: A system in accordance with Statement 21, wherein the integrity report includes a temperature range and a pressure range at which the well system will fail.

Statement 23: A system in accordance with Statement 21 or Statement 22, wherein the instructions further cause the processor to select a first trapped region from the one or more trapped annular regions; calculate an enclosure volume change for the first trapped region; and calculate an annular fluid expansion (AFE) of a well fluid contained within the enclosure of the first trapped region, the AFE corresponding to a fluid volume change caused by a temperature change.

Statement 24: A system in accordance with Statements 21-23, wherein the instructions further cause the processor to determine an annular pressure buildup (APB) corresponding to the first trapped region, wherein the enclosure volume change for the first trapped region is balanced with the AFE for the first trapped region.

Statement 25: A system in accordance with Statements 21-24, wherein the instructions further cause the processor to calculate a plurality of APBs corresponding to each of the plurality of initial temperatures and the plurality of final temperatures.

Statement 26: A system in accordance with Statements 21-25, wherein the instructions further cause the processor to calculate a respective enclosure volume change, a plurality of respective AFEs, and a plurality of respective APBs for each of the remaining one or more trapped annular regions.

Statement 27: A system in accordance with Statements 21-26, wherein the instructions further cause the processor to iteratively calculate a plurality of respective APBs for each of the one or more trapped annular regions assuming a non-rigid enclosure.

The embodiments shown and described above are only examples. Even though numerous characteristics and advantages of the present technology have been set forth in the foregoing description, together with details of the structure and function of the present disclosure, the disclosure is illustrative only, and changes may be made in the detail, especially in matters of shape, size and arrangement of the parts within the principles of the present disclosure to the full extent indicated by the broad general meaning of the terms used in the attached claims. It will therefore be appreciated that the embodiments described above may be modified within the scope of the appended claims. 

What is claimed is:
 1. A method for designing a well system envelop, the method comprising: creating an initial design for a well system including two or more tubing strings disposed within a well, the well system including one or more trapped annular regions therein, each of the one or more trapped annular regions including an enclosure; determining a plurality of initial temperatures, a plurality of final temperatures, and an initial pressure for each of the one or more trapped annular regions; estimating a final pressure for each of the one or more trapped annular regions; analyzing each of the one or more trapped annular regions; and generating a wellbore system envelop based at least in part on the analysis of each of the one or more trapped annular regions.
 2. The method of claim 1, wherein analyzing the one or more trapped annular regions further comprises: selecting a first trapped region from the one or more trapped annular regions; calculating an enclosure volume change for the first trapped region; and calculating an annular fluid expansion (AFE) of a well fluid contained within the enclosure of the first trapped region, the AFE corresponding to a fluid volume change caused by a temperature change.
 3. The method of claim 2, wherein analyzing the one or more trapped annular regions further comprises determining an annular pressure buildup (APB) corresponding to the first trapped region, wherein when the enclosure volume change for the first trapped region is balanced with the AFE for the first trapped region.
 4. The method of claim 3, further comprising calculating a plurality of APBs corresponding to each of the plurality of initial temperatures and the plurality of final temperatures.
 5. The method of claim 4, wherein when the well system further includes at least two casings the enclosure of the one or more trapped annular regions includes one or more casing enclosures between two casings, one or more casing and tubing enclosures between a casing and a tubing string, and one or more tubing enclosures between two tubing strings.
 6. The method of claim 4, further comprising calculating a respective enclosure volume change, a plurality of respective AFEs, and a plurality of respective APBs for each of the remaining one or more trapped annular regions.
 7. The method of claim 6, further comprising iterating the calculations of the plurality of respective APBs for each of the one or more trapped annular regions assuming a non-rigid enclosure.
 8. The method of claim 7, further comprising determining whether a global pressure of the well system is balanced for each of the one or more trapped annular regions within the well system based on the non-rigid enclosures.
 9. The method of claim 8, further comprising: generating a graphical representation of the of the wellbore system envelop showing a safe design limit, and transmitting the graphical representation to an output device.
 10. The method of claim 1, wherein the plurality of initial temperatures, the initial pressure, and the plurality of final temperatures for each of the one or more trapped annular regions are determined using calculations and/or simulation.
 11. A non-transitory computer-readable storage medium storing computer-executable instructions which, when executed by one or more processors, cause the one or more processors to: create initial design for a well system including two or more tubing strings disposed within a well, the well system including one or more trapped annular regions therein, each of the one or more trapped annular regions including an enclosure; determine a plurality of initial temperatures, a plurality of final temperatures, and an initial pressure for each of the one or more trapped annular regions; estimate a final pressure for each of the one or more trapped annular regions; analyze each of the one or more trapped annular regions; and generate a wellbore system envelop based at least in part on the analysis of each of the one or more trapped annular regions.
 12. The non-transitory computer-readable storage medium of claim 11, wherein the instructions further cause the processor to: select a first trapped region from the one or more trapped annular regions; calculate an enclosure volume change for the first trapped region; and calculate an annular fluid expansion (AFE) of a well fluid contained within the enclosure of the first trapped region, the AFE corresponding to a fluid volume change caused by a temperature change.
 13. The non-transitory computer-readable storage medium of claim 12, wherein the instructions further cause the processor to: determine an annular pressure buildup (APB) corresponding to the first trapped region, wherein the enclosure volume change for the first trapped region is balanced with the AFE for the first trapped region.
 14. The non-transitory computer-readable storage medium of claim 13, wherein the instructions further cause the processor to: calculate a plurality of APBs corresponding to each of the plurality of initial temperatures and the plurality of final temperatures.
 15. The non-transitory computer-readable storage medium of claim 14, wherein the instructions further cause the processor to: calculate a respective enclosure volume change, a plurality of respective AFEs, and a plurality of respective APBs for each of the remaining one or more trapped annular regions.
 16. The non-transitory computer-readable storage medium of claim 15, wherein the instructions further cause the processor to: iteratively calculate a plurality of respective APBs for each of the one or more trapped annular regions assuming a non-rigid enclosure.
 17. The non-transitory computer-readable storage medium of claim 16, wherein the instructions further cause the processor to: determine whether a global pressure of the well system is balanced for each of the one or more trapped annular regions within the well system based on the non-rigid enclosures.
 18. The non-transitory computer-readable storage medium of claim 17, wherein when the well system is balanced the instructions further cause the processor to: generate a graphical representation of the well system envelop showing a safe design limit; and display the well system envelop and the safe design limit on an output device communicatively coupled with the one or more processors.
 19. A system comprising: a well system including a wellbore having at least two tubing strings and at least one casing disposed therein, the well system including a plurality of trapped annular regions, each of the plurality of trapped annular regions being a non-rigid enclosure; one or more processors coupled with an input device; and at least one non-transitory computer-readable storage medium storing instructions which, when executed by the one or more processors, cause the one or more processors to: receive a plurality of initial temperatures, an initial pressure, and a plurality of final temperatures corresponding to each of the plurality of trapped annular regions from one or more sensors located within the wellbore of the well system; estimate a final pressure for each of the one or more trapped annular regions; analyze each of the one or more trapped annular regions; and generate an integrity report for the well system, wherein the integrity report is based at least in part on the analysis of each of the plurality of trapped annular regions.
 20. The system of claim 19, wherein the integrity report includes a temperature range and a pressure range at which the well system will fail. 